To employ the 1+1+2 Parikh-Wilczek [1]} decomposition of the metric we present the line element (REF ) in the following equivalent form:
\(ds^2=-\left(F_t dt+\omega d\varphi \right)^2+F_r^2 dr^2+\rho ^2(r,\theta ) d\theta ^2+\left(F^2_\varphi +\omega ^2 \right) d\varphi ^2,\) 
